eos7ca version 1.0: tough2 module for gas migration in

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LBNL-175204

EOS7CA Version 1.0:

TOUGH2 Module for Gas Migration in

Shallow Subsurface Porous Media Systems

Curtis M. Oldenburg

Earth Sciences Division Lawrence Berkeley National Laboratory

University of California Berkeley, CA 94720

March 6, 2015

This work was carried out as part of the Zero Emissions Research and Technology project funded

by the Assistant Secretary for Fossil Energy, Office of Coal and Power Systems through the National Energy Technology Laboratory, and by Lawrence Berkeley National Laboratory under

Department of Energy Contract No. DE-AC02-05CH11231.

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DISCLAIMER

This document was prepared as an account of work sponsored by the United States Government. While this document is believed to contain correct information, neither the United States Government nor any agency thereof, nor The Regents of the University of California, nor any of their employees, makes any warranty, express or implied, or assumes any legal responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by its trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof, or The Regents of the University of California. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof or The Regents of the University of California.

Ernest Orlando Lawrence Berkeley National Laboratory is an equal opportunity employer.

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Abstract

EOS7CA is a TOUGH2 module for mixtures of a non-condensible gas (NCG) and air

with or without a gas tracer, an aqueous phase, and water vapor. The user can select the NCG as

being CO2, N2, or CH4. EOS7CA uses a cubic equation of state with a multiphase version of

Darcy’s Law to model flow and transport of gas and aqueous phase mixtures over a range of

pressures and temperatures appropriate to shallow subsurface porous media systems. The

limitation to shallow systems arises from the use of Henry’s Law for gas solubility which is

appropriate for low pressures but begins to over-predict solubility starting at pressures greater

than approximately 1 MPa (10 bar). The components modeled in EOS7CA are water, brine,

NCG, gas tracer, air, and optional heat. The real gas properties module (ZEVCA) has options for

Peng-Robinson, Redlich-Kwong, or Soave-Redlich-Kwong equations of state to calculate gas

mixture density, enthalpy departure, and viscosity. Transport of the gaseous and dissolved

components is by advection and Fickian molecular diffusion. This user guide provides

instructions for use and two sample problems as verification and demonstration of EOS7CA.

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Contents

1. Introduction .............................................................................................................................. 9

2. Mathematical Formulation ................................................................................................... 10 2.1 General ............................................................................................................................... 10 2.2 Real Gas Mixture Properties .............................................................................................. 11

Density .................................................................................................................................. 11 Enthalpy ................................................................................................................................ 12 Viscosity................................................................................................................................ 13 Solubility of Gas Mixture Components ................................................................................ 13

2.3 Molecular Diffusion ........................................................................................................... 14

3. Implementing Real Gas Components ................................................................................... 15

4. Using EOS7CA ....................................................................................................................... 20 4.1 Compilation of EOS7CA ................................................................................................... 20 4.2 Input Formats ..................................................................................................................... 21

Single-phase conditions ................................................................................................ 22 Two-phase conditions ................................................................................................... 22

5. Example Problems ................................................................................................................. 26 5.1 SAM7CA1: Density, Viscosity, and Enthalpy of Real Gas Mixtures .............................. 26 5.2 SAM7CA2: CO2 Injection into a shallow vadose zone .................................................... 36

Introduction ........................................................................................................................... 36 Results and general description of CO2 migration ................................................................ 37

6. Final Notes .............................................................................................................................. 41

Acknowledgments ....................................................................................................................... 42

Nomenclature .............................................................................................................................. 42

References .................................................................................................................................... 44

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List of Figures

Figure 1. Example of self-documenting printout of key parameters in EOS7CA. ...................... 17

Figure 1. (continued). Example of self-documenting printout for EOS7CA. ............................. 18

Figure 2. Input file for SAM7CA1CO2. ...................................................................................... 29

Figure 2. (continued). Input file for SAM7CA1CO2. ................................................................. 30

Figure 3. Portions of output file for SAM7CA1CO2 showing results at various conditions. ..... 31

Figure 4. Input file SAM7CA2 for CO2 injection into shallow vadose zone. ............................. 38

Figure 5. Portion of output file for the shallow vadose zone problem SAM7CA2. .................... 39

Figure 6. EOS7CA simulation results for the SAM7CA2 vadose zone problem ........................ 40

List of Tables

Table 1. Module progression and enhancement. .......................................................................... 10

Table 2. Phases and components in EOS7CA (NCG = non-condensible gas). ........................... 11

Table 3. Molecular diffusivities for two phases and five components. ....................................... 25

Table 4. SAM7CA1 gas mixture conditions. NCG has been selected as CO2, N2, and CH4 ...... 28

Table 5. Properties of CO2-Air-H2O mixtures at 1 bar and 20 ˚C. .............................................. 32

Table 6. Properties of CO2-Air-H2O gas mixtures at 10 bars and 20 ˚C. .................................... 32

Table 7. Properties of N2-Air-H2O mixtures at 1 bar and 20 ˚C. ................................................. 33

Table 8. Properties of N2-Air-H2O gas mixtures at 10 bars and 20 ˚C. ....................................... 33

Table 9. Properties of CH4-Air-H2O mixtures at 1 bar and 20 ˚C. .............................................. 34

Table 10. Properties of CH4-Air-H2O gas mixtures at 10 bars and 20 ˚C. .................................. 34

Table 11. Enthalpy of CO2 (J kg-1) in gas mixture. ...................................................................... 35

Table 12. Enthalpy of N2 (J kg-1) in gas mixture. ........................................................................ 35

Table 13. Enthalpy of pure CH4 (J kg-1) in gas mixture. ............................................................. 35

Table 14. Properties of the homogeneous vadose zone. .............................................................. 37

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1. Introduction

The shallow subsurface is potentially vulnerable to impacts from carbon dioxide (CO2)

leakage up wellbores or permeable faults and fractures from geologic carbon sequestration sites.

In addition, methane (CH4) from deep sources or buried pipelines may migrate within the

shallow subsurface. The need to evaluate the flow and transport of leaking CO2 in the shallow

subsurface prompted the development of the simulation capabilities provided in

TOUGH2/EOS7CA. These capabilities for CO2 were then extended to include the choice

between CO2, N2, or CH4 as the NCG component that is modeled along with air which is always

present.

EOS7CA is related to a series of modules derived from the EOS3 module as shown in Table 1.

The starting point for development of EOS7CA was the radionuclide transport module EOS7R

(Oldenburg and Pruess, 1995; Pruess et al., 1999; 2011), to which we added capabilities for

modeling real gas mixtures such as CO2 and air. This report describes EOS7CA, the TOUGH2

module for simulating CO2 (or N2 or CH4) and air mixing processes in shallow subsurface porous

media systems. Applications of early versions of EOS7CA were published in Oldenburg and

Unger (2003), Oldenburg et al. (2010a,b), and Lewicki et al. (2009). The sample problems and

input format descriptions in the present report along with the TOUGH2 User’s Guide (Pruess et

al., 1999; 2011) provide sufficient information for using EOS7CA. EOS7C (Oldenburg et al.,

2004) is very similar to EOS7CA, except that it models methane (CH4) instead of air, and it has a

solubility model that is accurate for deep (high pressure) systems whereas the solubility model in

EOS7CA is limited to shallow (low pressure) systems.

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Table 1. Module progression and enhancement. TOUGH2 Module Components Added Capability EOS3 Water, air, heat EOS7 Water, brine, air, heat Dense brine EOS7R Water, brine, parent

radionuclide, daughter radionuclide, air, heat

Decay, adsorption, volatilization of radionuclides in trace concentrations.

EOS7CA Water, brine, NCG (CO2, N2, or CH4), gas tracer, air, heat

Real gas mixture properties, solubility model limited to low-pressure systems

EOS7C Water, brine, CO2 (or N2), gas tracer, CH4, heat

Real gas mixture properties and accurate solubility model for high-pressure systems

2. Mathematical Formulation

2.1 General

The general conservation equations solved in TOUGH2 for simulating multicomponent

and multiphase flow and transport in porous media are presented in Pruess et al. (1999; 2011)

along with a complete description of the theory and use of TOUGH2. In this report, we describe

EOS7CA and its specific methods and capabilities for modeling two phases and five components

plus heat in shallow subsurface systems. Table 2 shows the symbols and index numbers for the

phases and components in EOS7CA. The non-condensible gas (NCG) can be chosen by the user

as either carbon dioxide (CO2), nitrogen (N2), or methane (CH4) (see input parameter IE(16)).

Accurate density, viscosity, and enthalpy of the gas mixtures are included in EOS7CA through

the use of a real gas properties module ZEVCA as described below.

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Table 2. Phases and components in EOS7CA (NCG = non-condensible gas).

Phases (β) Components (κ)

1 – gas (g) 1 – water 2 – brine 3 – NCG 4 – tracer 5 – air

2 – aqueous (w) 1 – water 2 – brine 3 – NCG 4 – tracer 5 – air

2.2 Real Gas Mixture Properties

Density

EOS7CA makes use of a set of subroutines contained within a submodule called ZEVCA where

ZEV stands for Z factor, Enthalpy, and Viscosity, and CA indicates use with EOS7CA. These

subroutines are independently implemented in WebGasEOS, a publicly available webtool

(Reagan, 2006; http://esdtools.lbl.gov/gaseos/gaseos.html). ZEVCA calculates properties of real

gas mixtures using cubic equations of state, so-named because the volume terms are raised to

either the first, second, or third power (Reid et al., 1987). The most common two-parameter

equations of state can be written as

(1)

where the parameters and functions u, w, b, and a take on different values depending on the

particular cubic equation of state being used, and T is in degrees K. Other symbols are defined in

Nomenclature. Depending on user input (see input parameter IE(15)), EOS7CA can invoke Peng-

Robinson, Redlich-Kwong, or Soave-Redlich-Kwong cubic equations of state. Readers interested

in details of equations of state should consult Reid et al. (1987) and Poling et al. (2000) for more

information.

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The approach taken in EOS7CA is to use the equation of state to calculate the Z factor of the

mixture, where

(2)

From this value, the density of the gas mixture can be calculated using

TRZ

MWPV

nMW==ρ (3)

where the molecular weight (MW) is the molecular weight of the real gas mixture.

Enthalpy

Real-gas mixtures depart from ideality in ways that can be modeled with cubic equations of state.

The enthalpy of the real-gas mixtures is calculated using an ideal gas value with an added

enthalpy departure to account for real gas effects. In ZEVCA, we calculate enthalpy as

(4)

where (H – Hig) is the enthalpy departure. ZEVCA uses cubic equations of state (e.g., Peng-

Robinson) to calculate the enthalpy departures and ideal gas enthalpy change to come up with the

total enthalpy change of the real gas mixture.

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Standard TOUGH2 (Pruess et al., 1999; 2011) uses real-gas properties (steam tables) for steam

enthalpy, and thus produces more accurate steam enthalpies than the cubic equations of state can

provide. At user discretion (see input parameter IE(14)), the user can choose to use the steam

tables (subroutine SUPST) to calculate the enthalpy of the steam (water vapor) fraction in the

gas, and ZEVCA to calculate the enthalpy of the NCG and air mixture fraction. The total gas

mixture enthalpy is then calculated as a weighted combination of the SUPST and ZEVCA

contributions. The reference state for enthalpy calculations in ZEVCA is normalized to agree

with standard TOUGH2 and the NIST Chemistry Web Book (NIST, 2013), i.e., internal energy is

zero for saturated liquid at 273.16 K (0.01 ˚C).

Viscosity

Another important transport property for gas flow and transport is the viscosity of the real gas

mixture. ZEVCA uses the method of Chung et al. (1988) as described in Reid et al. (1987) and

Poling et al. (2000). This method is accurate to within 5-10% for the range of conditions

expected in subsurface natural gas reservoirs.

Solubility of Gas Mixture Components

Solubility of the gas components (i) is modeled using Henry’s Law, e.g.,

iaqh

i xKP i= (5)

where Khi is generally dependent on temperature. For the NCG component, the partial pressure of

the NCG, e.g., PCO2 for CO2, is related to the mole fraction of CO2 in the aqueous phase (xaqCO2)

by Henry’s Law where temperature dependence of Kh is calculated by the models of Cramer

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(1982), and D’Amore and Truesdell (1988) similar to the approach of TOUGH2/EWASG

(Battistelli et al., 1997). In EOS3, Khair was approximated as 1.0 x 1010 Pa, i.e., temperature

dependence was ignored for the solubility of air in water. In EOS7, salinity-dependence of Khair

was included by increasing Khair in aqueous solutions with higher brine mass fractions. EOS7CA

retains these EOS3 and EOS7 approaches to preserve continuity with EOS3 and EOS7, and

extends the methods by assuming for expediency that the same effects of brine on air solubility

occur also for NCG and tracer components. For example, if the Henry’s Law coefficient for air in

pure water and in brine at the local brine concentration are Kh,H2Oairand Kh,brine

air, respectively,

then the Henry’s Law coefficient for NCG in pure water at a given temperature would be

multiplied by the ratio Kh,brineair / Kh,H2O

air to obtain the value for the NCG Henry’s Law

coefficient at the given brine mass fraction. The Henry’s Law approach in EOS7CA is accurate

for low-pressure conditions (P < 10 bar or 1 MPa), but over predicts solubility at larger

pressures.

2.3 Molecular Diffusion

EOS7CA v. 1.0 includes binary diffusion of the chemical components dissolved in

aqueous and gas phases as discussed in the TOUGH2 User Guide (Pruess et al., 1999; 2011).

TOUGH2 includes pressure and temperature effects on gas-phase diffusion. Specifically,

molecular diffusivity is assumed to be inversely proportional to pressure (P) by the factor 1.0 ×

105/P (Pruess et al., 2011). For example, if pressure is 2 × 105 Pa, the corresponding effective

molecular diffusivity for the gas is one-half the input value which is referenced to 1.0 × 105 Pa.

This approach over-predicts diffusivity for CO2 mixtures above approximately 20 bars (Poling et

al., 2000, p. 11.16), with a total overprediction of a factor of two at P = 100 bars. Temperature

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effects on diffusion are also modeled by inclusion of the factor ((T + 273.15)/273.15)TEXP( see

TOUGH2 User Guide (Pruess et al., 2011)). If molecular diffusivity is input as a negative

number in TOUGH2, the absolute value of this number is used for the phase molecular

diffusivity without modification by pressure or temperature or S and τ (saturation and tortuosity)

Interested readers are referred to Pruess et al. (2011), Appendix D, for further details.

3. Implementing Real Gas Components

As shown in Table 1, EOS7CA was developed by changing the volatile radionuclide components

of EOS7R into a non-condensible gas (NCG) component (CO2, N2, or CH4, as specified by the

user through input parameter IE(16)), and a volatile tracer. One mole of air in EOS7CA is treated

internally as a mixture of 0.79 moles N2 and 0.21 moles O2 for calculation of gas mixture

properties in ZEVCA. The properties (density and viscosity) of the whole gas mixture containing

potentially water vapor, NCG, and air are calculated using ZEVCA (e.g., with Peng-Robinson

equation of state). The solubility of the gas components is modeled using Henry’s Law as

discussed in Section 2.2.

EOS7CA is designed for two-phase conditions (i.e., gas and aqueous phases present) in the

shallow subsurface and very limited testing has been done for single-phase conditions. In two-

phase conditions, vapor pressure is independent of salinity of the aqueous phase. As the brine

component is nonvolatile, vaporization would tend to increase brine mass fractions in the

aqueous phase beyond unity. Users need to be aware of this possibility, which arises from the

fact that EOS7CA, like EOS7, represents the aqueous phase as a mixture of water and brine, not

as a mixture of water and salt. Therefore, EOS7CA cannot be used for processes in which

solubility limits would be reached, at which point solid salt would precipitate. The tracer

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component in EOS7CA does not affect gas properties and is expected to exist only in trace

concentrations (e.g., mass fractions of order 10-6). A summary of EOS7CA specifications is

printed upon execution and is reproduced here in Fig. 1.

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*********************************************************************************************************************************** * EOS7CA: EQUATION OF STATE FOR MIXTURES OF WATER/BRINE/NON-CONDENSIBLE GAS/TRACER/AIR * *********************************************************************************************************************************** EQUATION OF STATE: PR (IE(15) = 1) NON-CONDENSIBLE GAS: CO2 (IE(16) = 1) OPTIONS SELECTED ARE: (NK,NEQ,NPH,NB,NKIN) = (5,6,2,8,5) NK = 5 - NUMBER OF COMPONENTS NEQ = 6 - NUMBER OF EQUATIONS PER GRID BLOCK NPH = 2 - NUMBER OF PHASES THAT CAN BE PRESENT NB = 8 - NUMBER OF SECONDARY PARAMETERS (OTHER THAN' COMPONENT MASS FRACTIONS) NKIN = 5 - number of components for initializing thermodynamic conditions (default is NKIN = NK) For NB = 6, diffusion is "off", for NB = 8, diffusion is "on" AVAILABLE OPTIONS for (NK,NEQ,NPH,NB): (5,5,2,6 or 8) - WATER, BRINE, NCG, TRC, AIR; ISOTHERMAL; VARIABLES (P, XB, XNCG, XTRC, X OR S+10, T) (5,6,2,6 or 8) - WATER, BRINE, NCG, TRC, AIR; NON-ISOTHERMAL; VARIABLES (P, XB, XNCG, XTRC, X OR S+10, T) (4,4,2,6 or 8) - WATER, BRINE, NCG, TRC, NO AIR; ISOTHERMAL; VARIABLES (P, XB, XNCG, XTRC, T) (4,5,2,6 or 8) - WATER, BRINE, NCG, TRC, NO AIR; NON-ISOTHERMAL; VARIABLES (P, XB, XNCG, XTRC, T) NKIN = NK or NKIN = NK-2. Default options are (5,5,2,8) - isothermal, diffusion "on", NKIN=NK THE NK = 4 ("NO AIR") OPTIONS MAY ONLY BE USED FOR PROBLEMS WITH SINGLE-PHASE LIQUID CONDITIONS THROUGHOUT. THE NORMAL NUMBER OF SECONDARY PARAMETERS OTHER THAN MASS FRACTIONS IS 6 PER PHASE. IN EOS7CA, WE OPTIONALLY ADD TO THIS A SATURATION-DEPENDENT TORTUOSITY FOR EACH PHASE, AS WELL AS TEMPERATURE AND PRESSURE DEPENDENCE OF THE DIFFUSION COEFFICIENT. *********************************************************************************************************************************** NKIN = 5 *** ALLOWS INITIALIZATION WITH DIFFERENT SETS OF PRIMARY VARIABLES. *** *** THIS IS USEFUL FOR STARTING EOS7CA SIMULATIONS FROM EOS7 INITIAL CONDITIONS. *** = NK (default): (P,XB,XNCG,XTRC,XAIR,T) FOR SINGLE PHASE, (P,XB,XNCG,XTRC,S+10,T) FOR TWO-PHASE. (EOS7CA FORMAT). = NK-2: (P,XB,XAIR,T) FOR SINGLE PHASE, (P,XB,S+10,T) FOR TWO-PHASE. (EOS7 FORMAT). WILL INITIALIZE XNCG = XTRC = 0. MOP(20) = 0 *** CONTROLS HANDLING OF NEGATIVE AIR MASS FRACTIONS. = 0: DO NOT INCREASE PRESSURE TO AVOID NEGATIVE AIR MASS FRACTIONS = 1: INCREASE PRESSURE TO AVOID NEGATIVE AIR MASS FRACTIONS IE(14) = 1 *** CONTROLS CALCULATION OF GAS ENTHALPY = 0: USE SUPST FOR VAPOR, ZEVCA FOR NCG AND AIR = 1: USE ZEVCA FOR THE WHOLE MIXTURE ***********************************************************************************************************************************

Figure 1. Self-documenting printout of key parameters for specifying components and phases in EOS7CA.

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THE PRIMARY VARIABLES ARE P - PRESSURE T - TEMPERATURE XB - BRINE MASS FRACTION XNCG - MASS FRACTION OF NON-CONDENSIBLE GAS XTRC - MASS FRACTION OF VOLATILE TRACER S+10. - (GAS PHASE SATURATION + 10.) X - AIR MASS FRACTION IN GAS T - TEMPERATURE ****************************** ***************************************************************** * COMPONENTS * * FLUID PHASE CONDITION PRIMARY VARIABLES * ****************************** ***************************************************************** * * * * * # 1 - WATER * * SINGLE-PHASE GAS (#) P, XB, XNCG, XTRC, X, T * * * * * * # 2 - BRINE * * SINGLE-PHASE LIQUID (*) P, XB, XNCG, XTRC, X, T * * * * * * # 3 - NCG * * TWO-PHASE (*) P, XB, XNCG, XTRC, S+10., T * * * * * * # 4 - TRC * ***************************************************************** * * (#) XB, XNCG, XTRC AND X ARE MASS FRACTIONS IN THE GAS PHASE. * # 5 - AIR * (*) XB, XNCG, XTRC AND X ARE MASS FRACTIONS IN THE AQUEOUS PHASE. * * * # 6 - HEAT * * * *********************************************************************************************************************************** BRINE PROPERTIES DENSITY = 0.118500E+04 KG/M**3 AT REFERENCE CONDITIONS OF (P,T) = (0.100000E+06 PA,0.200000E+02 DEG-C) COEFFICIENTS FOR BRINE VISCOSITY ARE: VCO(I) = 0.481900E+00 -.277400E+00 0.781400E+00 PROPERTIES OF NCG AND TRACER: DOMAIN NCG TRC HALF-LIFE (SECONDS): -ALL- NO DECAY 0.1000E+51 MOLECULAR WEIGHT (GM/MOLE): -ALL- 0.4400E+02 0.2300E+03 INVERSE HENRY CONST.(MOLE/PA): -ALL- VARIABLE 0.5700E-10 HEAT CAPACITY (J/(KG K)): -ALL- 0.8240E+03 NEGLIGIBLE GAS PHASE DIFFUSIVITY (M**2/S): -ALL- 0.1000E-04 0.1000E-04 AQ. PHASE DIFFUSIVITY (M**2/S): -ALL- 0.1000E-09 0.1000E-09 DISTRIBUTION COEFF. (M**3/KG): rock 0.0000E+00 0.0000E+00 MOLECULAR DIFFUSIVITY OF WATER, BRINE, NCG, TRC, AND AIR THROUGH THE GASEOUS AND AQUEOUS PHASES, (FDDIAG(PHASE,COMP)) [M**2/S]: PHASE 1 = GAS; PHASE 2 = AQUEOUS PHASE COMP PHASE COMP PHASE COMP PHASE COMP PHASE COMP PHASE COMP PHASE COMP PHASE COMP PHASE COMP PHASE COMP -1- -1- -1- -2- -1- -3- -1- -4- -1- -5- -2- -1- -2- -2- -2- -3- -2- -4- -2- -5- 0.10000E-04 0.00000E+00 0.10000E-04 0.10000E-04 0.10000E-04 0.10000E-09 0.00000E+00 0.10000E-09 0.10000E-09 0.10000E-09 Figure 1. (continued). Example of self-documenting printout for EOS7CA.

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4. Using EOS7CA

4.1 Compilation of EOS7CA

As an extension of TOUGH2, EOS7CA consists of all of the TOUGH2 V2.1 subroutines and the

new equation of state module EOS7CA subroutines and ZEVCA subroutines. Typical

compilation on a LINUX workstation with the Portland Group Fortran compiler, for example,

would be as follows:

pgf77 –c –r8 –i8 t2fm.f t2cg22.f t2f.f t2solv.f meshm.f eos7cav1.f zevcav1.f

pgf77 –o x7ca t2fm.o t2cg22.o t2f.o t2solv.o meshm.o eos7cav1.o zevcav1.o

A GFortran Makefile is as follows:

#Makefile objects = t2fm.o t2cg22.o t2f.o t2solv.o meshm.o eos7cav1.o zevcav1.o FC = gfortran FFLAGS = -g -freal-4-real-8 -fno-align-commons -std=legacy x7ca: $(objects) $(FC) -o x7ca $(objects) %o.: %.f %(FC) $(FFLAGS) -c $<

The italics indicate the new program units of EOS7CA.

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4.2 Input Formats

Below we describe the input formats for specifying EOS7CA-specific input. Other

TOUGH2 input parameter formats are given in Pruess et al. (2011). EOS7CA-specific input

parameters are provided through the MULTI block, SELEC block and PARAM block.

MULTI format(4I5)

NK, NEQ, NPH, NB, NKIN

NK Set NK = 5 for water, brine, NCG, gas tracer, and air.

NEQ Number of equations per grid block.

Set NEQ = NK for isothermal problems.

Set NEQ = NK + 1 for nonisothermal problems.

NPH Number of phases. Set NPH = 2.

NB Number of secondary parameters. Set NB = 6 for no-diffusion,

NB = 8 for diffusion on.

NKIN Number of mass components in INCON (default is NKIN = NK).

This parameter can be used to initialize EOS7CA run (NK = 4 or

5) with EOS7 (NK = 2 or 3) INCON data, in which case NCG and

tracer (components 3 and 4) are initialized with Xg,lκ = 0.

PARAM.1 format(2I2, 3I4, 24I1, 10X, 2E10.4)

NOITE, KDATA, MCYC, MSEC, MCYPR, (MOP(I), I = 1, 24), TEXP, BE

See TOUGH2 User Guide (Pruess et al., 1999; 2011) or TOUGH2

informative printout for description of all of the above parameters

except the following:

MOP(20) Option for resetting variables.1

0: Variables are not reset if partial pressures exceed total pressure.

1: Pressure is reset to sum of partial pressures if partial pressures

exceed total pressure.

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1This option is needed because in some cases, the sum of partial pressures exceeds the total

pressure, e.g., if temperature changes cause rapid exsolution of dissolved gases. When this

occurs, erroneous negative mass fractions can arise. In this case, setting MOP(20) = 1 can

alleviate the problem. However, as a default, we recommend setting MOP(20) = 0, as this

problem is not often encountered.

PARAM.4 primary variables used for default conditions for all grid blocks that are not

assigned by means of data blocks INDOM or INCON. Option START

isnecessary to invoke these default initial conditions for grid blocks (for additional

information, see the TOUGH2 User Guide description of keyword PARAM.4).

Two lines will be read for the six primary variables in EOS7CA. See INCON

description for primary variable description.

PARAM.4 format(4E20.14)

DEP(I), I = 1,6

INCON introduces grid block-specific initial conditions. Two lines will be read per

grid block for the six primary variables in EOS7CA.

INCON.1 format(4E20.14,/,2E20.4)

DEP(I), I = 1,6

DEP(I) are the primary variables as follows:

Single-phase conditions

(P, Xbrine, Xncg, Xtrc, Xair, T) where P is pressure, Xbrine is always brine mass fraction in the liquid

phase, other X’s are mass fractions in gas or liquid phase, and T is temperature in ˚C.

Two-phase conditions

(P, Xbrineliq, Xncg

liq, Xtrcliq, S + 10, T) where P is gas-phase pressure, X’s are brine, NCG, and TRC

mass fractions in the liquid, S is gas saturation, and T is temperature in ˚C

SELEC keyword to introduce a data block with reference brine and NCG input data.

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SELEC.1 format(8I5)

IE(1), NGBINP(1), NGBINP(2), NGBINP(3), NFBL, NFBR, NFBT, NFBB

IE(1) Set equal to 6 to read six additional data records.

IE(14) Set equal to 0 to use ZEVCA for enthalpy of gas mixture,

Set equal to 1 to use SUPST for water vapor, and ZEVCA for

NCG and air, with a weighted sum used for the mixture enthalpy.

IE(15) Set equal to 1 for Peng-Robinson (PR) equation of state;

Set equal to 2 for Redlich-Kwong (RK) equation of state;

Set equal to 3 for Soave-Redlich-Kwong (SRK) equation of state.

IE(16) Set equal to 1 for NCG = CO2,

Set equal to 2 for NCG = N2,

Set equal to 3 for NCG = CH4.

SELEC.2 format(3E10.4) (unchanged from standard EOS7)

P0, T0, ρ0

P0 Reference pressure, in Pa

T0 Reference temperature, in ˚C

ρ0 Brine density at (P0, T0), in kg m-3.

For P0, T0, ρ0 equal to zero or blank, default values of P0 = 1 ×

105 Pa, T0 = 25 ˚C, and ρ0 = 1185.1 kg m-3 will be used. For P0 <

0, brine will be assumed to be pure water. This allows modeling of

flow with two waters that differ only in trace constituents, but have

identical thermophysical properties.

SELEC.3 format(3E10.4) (unchanged from standard EOS7)

v(i), i = 1,3

v(i) Coefficients for salinity correction in aqueous phase viscosity (see

Pruess et al., 1999, p. 41). If v(i) =0 for i = 1, 2, 3, default values

will be used: v(1) = 0.4819, v(2) = -0.2774, v(3) = 0.7814.

Specification of brine as pure water in record SELEC.2 will

override viscosity specifications and will always result in viscosity

of pure water being used.

24 Rev. 1.1

SELEC.4 format(7E10.4)

Leave this line blank.






blank, XMW(4), blank, blank, blank, blank, HCTRC

XMW(4) Molecular weight of tracer component 4, in g/mole.

HCTRC Inverse Henry's constant for gas tracer (component 4), in Pa-1 .

DIFFU format(2E10.4)

FDDIAG(1,1),FDDIAG(2,1)





Molecular diffusivity of components 1–5 in phases 1, 2 (gas and

liquid) in m2 s-1. If FDDIAG(NP,NK) is input as a negative

number, the absolute value is used for the phase molecular

diffusivity ( ) without modification by S and τ (saturation and

tortuosity) and without pressure or temperature effects in the case

of gas diffusivity.

25 Rev. 1.1

Table 3. Molecular diffusivities for two phases and five components.

Phase Component (NP,NK) Input Units

Gaseous Water Brine NCG Tracer Air

(1,1) (1,2) (1,3) (1,4) (1,5)

DIFFU(1,1) DIFFU(1,2) DIFFU(1,3) DIFFU(1,4) DIFFU(1,5)

m2 s-1 m2 s-1

m2 s-1

m2 s-1

m2 s-1

Aqueous Water Brine NCG Tracer Air

(2,1) (2,2) (2,3) (2,4) (2,5)

DIFFU(2,1) DIFFU(2,2) DIFFU(2,3) DIFFU(2,4) DIFFU(2,5)

m2 s-1 m2 s-1

m2 s-1

m2 s-1

m2 s-1

26 Rev. 1.1

5. Example Problems

5.1 SAM7CA1: Density, Viscosity, and Enthalpy of Real Gas Mixtures

In this section, we present results from a simple test problem designed to demonstrate the gas

mixture property calculations of EOS7CA v. 1.0 through comparison of computed properties

with independent reference values. The domain consists of six grid blocks arranged in two

columns with three rows. The various conditions are shown in Table 4.

The input file for SAM7C1 for NCG = CO2 is shown in Figure 2. A partial output file is shown

in Figure 3. Note the first three letters of the grid block name suggests the compositions in each

grid block, while the last two numbers give the row and column, respectively. In Tables 5-13,

we present a summary of the results and comparisons to standard reference values.

The first comparison we present is for density (ρ) and viscosity (µ) of the NCG–air mixture at

20 oC and 1 and 10 bars (Tables 5-10). For brevity, we present in Tables 5-10 physical properties

only for the end members and 50-50 mole fraction mixtures. We have included reference values

either from the NIST Chemistry WebBook (NIST, 2013), or from WebGasEOS (Reagan, 2006).

Note that the EOS7CA output file gives compositions in terms of mass fraction (X), whereas the

compositions in the tables are specified in terms of mole fractions in the gas (xg) phase for

consistency with the reference sources. The conversions from mass fraction to mole fraction are

given by the equations

27 Rev. 1.1

(6)

(7).

Note further in Tables 5-13 that for these two-phase conditions with water present, there is a

small amount of water vapor in the gas phase that is not present in the reference calculations. As

shown in Tables 5-10 for CO2, N2, and CH4, EOS7CA approximates gas mixture properties very

well.

In Tables 11-13, we present comparisons of enthalpy calculations using the IE(14) = 1 option,

i.e., SUPST for steam fraction and ZEVCA for CO2 and air fractions. This approach appears to

be acceptable as shown by comparing EOS7CA estimates against NIST Chemistry WebBook

values.

28 Rev. 1.1

Table 4. SAM7CA1 gas mixture conditions. NCG can be selected as CO2, N2, or CH4.

Two-Phase P = 1 bar T = 20 ˚C

Two-Phase P = 10 bar T = 20 ˚C

xgNCG = 1.0

xgAir = 0.0

xgH2O = trace

xg

NCG = 1.0 xg

Air = 0.0 xg

H2O = trace

xg

NCG = 0.5 xg

Air = 0.5 xg

H2O = trace

xg

NCG = 0.5 xg

Air = 0.5 xg

H2O = trace

xg

NCG = 0.0 xg

Air = 1.0 xg

H2O = trace

xg

NCG = 0.0 xg

Air = 1.0 xg

H2O = trace

29 Rev. 1.1

*SAM7CA1CO2* ... Verification problem for EOS7CA. ROCKS----1----*----2----*----3----*----4----*----5----*----6----*----7----*----8 rock 2 2600. .20 1.e-12 1.e-12 1.e-12 2.51 1000. 0.25 7 0.20 .27 1. 0.01 7 0.20 .25 .00084 1.e5 1. MULTI----1----*----2----*----3----*----4----*----5----*----6----*----7----*----8 5 6 2 8 START----1----*----2----*----3----*----4----*----5----*----6----*----7----*----8 ----*----1 MOP: 123456789*123456789*1234 ---*----5----*----6----*----7----*----8 PARAM----1----*----2----*----3----*----4----*----5----*----6----*----7----*----8 3 1 110 090000020000400 3 -1. 9.8066 1.e-9 1.e-5 1.000e5 0. 0.e-1 0.e-4 10.500 20. IE(14) = 1, use SUPST & ZEVCA for enthalpy. IE(14) = 0, use ZEVCA only. IE(15) = 1, use Peng-Robinson eqn. of state. IE(15) = 2,3 use RK,SRK, resp. IE(16) = 1, 2, or 3 NCG is CO2, N2, or CH4, respectively. SELEC----1----*----2----*----3----*----4----*----5----*----6----*----7----*----8 6 1 1 1 -1.e5 1.e50 230.00 0.0 0.0 0.0 0.0 5.70e-11 diffusivity data are input as follows: first row: water (gas, liq.) second row: brine (gas, liq.) third row: ncg (gas, liq.) fourth row: trc (gas, liq.) fifth row: ch4 (gas, liq.) DIFFU----1----*----2----*----3----*----4----*----5----*----6----*----7----*----8 1.e-5 1.e-10 0.e-6 0.e-6 1.e-5 1.e-10 1.e-5 1.e-10 1.e-5 1.e-10

Figure 2. Input file for SAM7CA1CO2.

30 Rev. 1.1

INCON----1----*----2----*----3----*----4----*----5----*----6----*----7----*----8 CO211 1.000e5 0. 0.00164 0.e-4 10.50 20. MIX21 1.000e5 0. 0.000849 0.e-4 10.50 20. AIR31 1.000e5 0. 0.0000 0.e-4 10.50 20. CO212 1.000e6 0. 0.0164 0.e-4 10.50 20. MIX22 1.000e6 0. 0.00852 0.e-4 10.50 20. AIR32 1.000e6 0. 0.0000 0.e-4 10.50 20. ELEME----1----*----2----*----3----*----4----*----5----*----6----*----7----*----8 CO211 10.1000E+010.1000E+01 0.5000E+000.5000E+00-.5000E+00 MIX21 10.1000E+010.0000E+00 0.5000E+000.5000E+00-.1500E+01 AIR31 10.1000E+010.1000E+01 0.5000E+000.5000E+00-.2500E+01 CO212 10.1000E+010.1000E+01 0.5000E+000.1500E+01-.5000E+00 MIX22 10.1000E+010.0000E+00 0.5000E+000.1500E+01-.1500E+01 AIR32 10.1000E+010.1000E+01 0.5000E+000.1500E+01-.2500E+01 CONNE ENDCY----1----*----2----*----3----*----4----*----5----*----6----*----7----*----8

Figure 2. (continued). Input file for SAM7CA1CO2.

31 Rev. 1.1

*SAM7CA1CO2* ... Verification problem for EOS7CA. OUTPUT DATA AFTER ( 1, 1)-2-TIME STEPS THE TIME IS 0.115741E-13 DAYS @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ TOTAL TIME KCYC ITER ITERC KON DX1M DX2M DX3M MAX. RES. NER KER DELTEX 0.100000E-08 1 1 1 2 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 1 1 0.10000E-08 @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ NCG = CO2 ELEM. INDEX P T SL XBRINE(LIQ) XNCG(LIQ) XAIR(LIQ) XAIR(GAS) XNCG(GAS) XTRC(GAS) DG (PA) (DEG-C) (KG/M**3) CO211 1 0.10000E+06 0.20000E+02 0.50000E+00 0.00000E+00 0.16400E-02 0.52586E-07 0.21880E-02 0.98815E+00 0.00000E+00 0.17886E+01 MIX21 2 0.10000E+06 0.20000E+02 0.50000E+00 0.00000E+00 0.84900E-03 0.75991E-05 0.37756E+00 0.61085E+00 0.00000E+00 0.14921E+01 AIR31 3 0.10000E+06 0.20000E+02 0.50000E+00 0.00000E+00 0.00000E+00 0.15699E-04 0.98532E+00 0.00000E+00 0.00000E+00 0.11779E+01 CO212 4 0.10000E+07 0.20000E+02 0.50000E+00 0.00000E+00 0.16400E-01 0.25049E-05 0.10428E-01 0.98866E+00 0.00000E+00 0.19033E+02 MIX22 5 0.10000E+07 0.20000E+02 0.50000E+00 0.00000E+00 0.85200E-02 0.78353E-04 0.38796E+00 0.61091E+00 0.00000E+00 0.15359E+02 AIR32 6 0.10000E+07 0.20000E+02 0.50000E+00 0.00000E+00 0.00000E+00 0.16036E-03 0.99855E+00 0.00000E+00 0.00000E+00 0.11887E+02 @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@

.

.

. @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ ^L *SAM7CA1CO2* ... Verification problem for EOS7CA. KCYC = 1 - ITER = 1 - TIME =0.100000E-08 ELEM. INDEX P T SL DX1 DX2 H(GAS) pncg/px K(GAS) K(LIQ.) VIS(GAS) (J/KG) (PA S) CO211 1 0.10000E+06 0.20000E+02 0.50000E+00 0.00000E+00 0.00000E+00 0.51697E+06 0.97336E+00 0.41589E+00 0.21697E-06 0.14366E-04 MIX21 2 0.10000E+06 0.20000E+02 0.50000E+00 0.00000E+00 0.00000E+00 0.44386E+06 0.50366E+00 0.41589E+00 0.21697E-06 0.16973E-04 AIR31 3 0.10000E+06 0.20000E+02 0.50000E+00 0.00000E+00 0.00000E+00 0.32514E+06 0.00000E+00 0.41589E+00 0.21697E-06 0.20032E-04 CO212 4 0.10000E+07 0.20000E+02 0.50000E+00 0.00000E+00 0.00000E+00 0.48832E+06 0.98193E+00 0.41589E+00 0.21697E-06 0.14750E-04 MIX22 5 0.10000E+07 0.20000E+02 0.50000E+00 0.00000E+00 0.00000E+00 0.41540E+06 0.50775E+00 0.41589E+00 0.21697E-06 0.17379E-04 AIR32 6 0.10000E+07 0.20000E+02 0.50000E+00 0.00000E+00 0.00000E+00 0.29391E+06 0.00000E+00 0.41589E+00 0.21697E-06 0.20444E-04 @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@

Figure 3. Portions of output file for SAM7CA1CO2 showing results at various conditions.

32 Rev. 1.1

Table 5. Properties of CO2-Air-H2O mixtures at 1 bar and 20 ˚C. gas phase

xgAir xg

CO2 ρ (kg m-3) µ (Pa s)

EOS7CA 3.26 × 10-3 0.973 1.79 1.44 × 10-5

Reference1,2 0. 1. 1.81 1.47 × 10-5

EOS7CA 0.496 0.504 1.49 1.70 × 10-5

Reference3 0.5 0.5 1.50 1.65 × 10-5

EOS7CA 0.977 0. 1.18 2.00 × 10-5

Reference1,2 1. 0. 1.15 1.76 × 10-5 1NIST Chemistry WebBook thermophysical properties, 2013 2Air approximated as N2 in NIST Chemistry WebBook 3Mixture approximated as 0.395-0.105-0.5 mole fraction N2-O2-CH4 mixture in WebGasEOS. Table 6. Properties of CO2-Air-H2O gas mixtures at 10 bars and 20 ˚C. gas phase

xgAir xg

CO2 ρ (kg m-3) µ (Pa s)

EOS7CA 1.57 × 10-2 0.982 19.03 1.47 × 10-5

Reference1,2 0. 1. 19.10 1.48 × 10-5

EOS7CA 0.490 0.510 15.36 1.74 × 10-5

Reference3 0.5 0.5 15.36 1.66 × 10-5

EOS7CA 0.998 0. 11.89 2.04 × 10-5

Reference1,2 1. 0. 11.52 1.77 × 10-5 1NIST Chemistry Webbook thermophysical properties webtool, 2013 2Air approximated as N2 in NIST Chemistry WebBook 3Mixture approximated as 0.395-0.105-0.5 mole fraction N2-O2-CH4 mixture in WebGasEOS.

33 Rev. 1.1

Table 7. Properties of N2-Air-H2O mixtures at 1 bar and 20 ˚C. gas phase

xgAir xg

N2 ρ (kg m-3) µ (Pa s)

EOS7CA 3.64 × 10-3 0.973 1.14 1.72 × 10-5

Reference1,2 0. 1. 1.15 1.76 × 10-5

EOS7CA 0.471 0.505 1.16 1.85 × 10-5

Reference3 0.5 0.5 1.17 1.77 × 10-5

EOS7CA 0.977 0. 1.18 2.00 × 10-5

Reference1,2 1. 0. 1.15 1.76 × 10-5 1NIST Chemistry Webbook thermophysical properties webtool, 2013 2Air approximated as N2 in NIST Chemistry WebBook 3Mixture approximated as 0.395-0.105-0.5 mole fraction N2-O2-CH4 mixture in WebGasEOS. Table 8. Properties of N2-Air-H2O gas mixtures at 10 bars and 20 ˚C. gas phase

xgAir xg

N2 ρ (kg m-3) µ (Pa s)

EOS7CA 1.93 × 10-2 0.978

11.54 1.76 × 10-5

Reference1,2 0. 1. 11.52 1.77 × 10-5

EOS7CA 0.490 0.510 11.71 1.88 × 10-5

Reference3 0.5 0.5 11.73 1.78 × 10-5

EOS7CA 0.998 0. 11.89 2.04 × 10-5


34 Rev. 1.1

Table 9. Properties of CH4-Air-H2O mixtures at 1 bar and 20 ˚C. gas phase

xgAir xg

CH4 ρ (kg m-3) µ (Pa s)

EOS7CA 6.21 × 10-3 0.970 0.663 1.10 × 10-5

Reference1,2 0. 1. 0.659 1.10 × 10-5

EOS7CA 0.472 0.504 0.911 1.39 × 10-5

Reference3 0.5 0.5 0.922 1.37 × 10-5

EOS7CA 0.977 0. 1.18 2.00 × 10-5

Reference1,2 1. 0. 1.15 1.76 × 10-5 1NIST Chemistry Webbook thermophysical properties webtool, 2013 2Air approximated as N2 in NIST Chemistry WebBook 3Mixture approximated as 0.395-0.105-0.5 mole fraction N2-O2-CH4 mixture in WebGasEOS. Table 10. Properties of CH4-Air-H2O gas mixtures at 10 bars and 20 ˚C. gas phase

xgAir xg

CH4 ρ (kg m-3) µ (Pa s)

EOS7CA 9.45 × 10-3 0.988

6.77 1.11 × 10-5

Reference1,2 0. 1. 6.70 1.11 × 10-5

EOS7CA 0.490 0.508 9.26 1.41 × 10-5

Reference3 0.5 0.5 9.32 1.37 × 10-5

EOS7CA 0.998 0. 11.89 2.04 × 10-5


35 Rev. 1.1

Table 11. Enthalpy of CO2 (J kg-1) in gas mixture. 1.0 bar

20 ˚C2 10 bar 20 ˚C3

EOS7CA 5.170 × 105 4.883 × 105 Reference1 5.016 × 105 4.925 × 105 1NIST Standard Reference Database 69 – March 2003 Release: NIST Chemistry WebBook. 2xg

CO2 = 0.973 in EOS7CA, xgCO2 = 1.0 in NIST reference case.

3xgCO2 = 0.982 in EOS7CA, xg

CO2 = 1.0 in NIST reference case. Table 12. Enthalpy of N2 (J kg-1) in gas mixture. 1.0 bar

20 ˚C2 10 bar 20 ˚C3


N2 = 0.973 in EOS7CA, xgN2 = 1.0 in NIST reference case.

3xgN2 = 0.978 in EOS7CA, xg

N2 = 1.0 in NIST reference case. Table 13. Enthalpy of pure CH4 (J kg-1) in gas mixture. 1.0 bar

20 ˚C2 10 bar 20 ˚C3


CH4 = 0.970 in EOS7CA, xgCH4 = 1.0 in NIST reference case.

3xgCH4 = 0.988 in EOS7CA, xg

CH4 = 1.0 in NIST reference case.

36 Rev. 1.1

5.2 SAM7CA2: CO2 Injection into a Shallow Vadose Zone

Introduction

This test problem is prototypical of the kinds of injection and migration problems that EOS7CA

was designed to handle. The problem consists of a shallow vadose zone with a water table at a

depth of approximately 3 m. We assume there is a horizontal injection well at a depth of

approximately 2.4 m, and that the well is long enough that the flow domain can be approximated

as a two-dimensional (2D) Cartesian slice transverse (perpendicular) to the well. This test

problem is designed to model field experiments aimed at studying how CO2 will flow and

migrate within the shallow subsurface following its arrival from a deep leaking geologic carbon

sequestration site through a leakage pathway such as an abandoned well, fault, or fracture zone

(e.g., Oldenburg et al., 2010a). Table 1 provides properties of the system, and Figure 4 shows the

input file. Figure 5 shows excerpts from the EOS7CA output file for this run.

Figure 6a shows the Cartesian 2D transverse model system discretization and water table

location. The top boundary is held at a constant pressure of 1 bar (105 Pa), zero CO2

concentration, and 15 oC temperature. The right-hand side boundary is held at constant

conditions corresponding to the initial condition which has a gravity-capillary equilibrium above

the water table and liquid saturation equal to 0.5 at the top of the domain. The bottom boundary

of the system is held at constant (aqueous-phase) fully saturated conditions and P = 1.194 bar

(i.e., hydrostatic below the initial water table). The left-hand side boundary is closed to flow

representing a mirror symmetry plane.

37 Rev. 1.1

Results and general description of CO2 migration

Figure 6b-d shows model results for three times during simulation of CO2 injection from the

horizontal well with an injection rate of 2.43 kg d-1. As shown in Figure 6, the CO2 exits the well

directly into the unsaturated zone and creates a CO2-rich zone around the well. The CO2 spreads

in all directions by pressure-gradient driving forces. Note the CO2 gas pushes the water table

down as shown by the deflection of the light-blue contour lines, and by the high CO2

concentration in the gas where formerly saturated aqueous phase conditions prevailed. The CO2

exits out the ground surface (top of model domain) at some time between 0.5 and 1 day. By 5

days, the region of CO2 flux out the ground surface extends to more than 3 m from the trace of

the well. Note the high mass fractions of CO2 in the gas phase (nearly pure CO2) consistent with

prior results of leakage and seepage modeling (Oldenburg and Unger, 2003), and high soil-gas

concentration gradient near the ground surface.

Table 14. Properties of the homogeneous vadose zone. Soil Temperature (T) 15 oC Porosity (φ) 0.30 Permeability (k) 1 × 10-12 m2 Capillary Pressure (Pc) van Genuchten1,2

λ = 0.2, Slr = 0.11, α = 8.5 × 10-4 Pa-1, Pmax = 1 × 1010 Pa, Sls = 1.

Relative permeability (kr) van Genuchten1,2 Slr = 0.10, Sgr = 0.01

Molec. diffusivity coefficients (dβκ)

Liquid: 10-10 m2 s-1 Gas: 10-5 m2 s-1

θ = 1.0, P0 = 105 Pa Tortuosity (τ0) 1.0 Saturation-dependent tortuosity (τβ) Equal to relative

permeability 1Pruess et al. (1999; 2011) 2λ is m in van Genuchten (1980).

38 Rev. 1.1

simple soil for shallow CO2 release by perforated pipe. ROCKS----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8 vados 2 2400. 0.3 1.00E-12 1.00E-12 1.00E-12 1.73 935.8 1.00E-10 1. 7 0.2 0.1 1. 0.01 7 0.2 0.11 8.5e-4 1.e10 1. tpbnd 2 2400. 0.3 1.00E-12 1.00E-12 1.00E-12 1.73 1.e5 1.00E-10 1. 7 0.2 0.1 1. 0.01 7 0.2 0.11 8.5e-4 1.e10 1. btbnd 2 2400. 0.3 1.00E-12 1.00E-12 1.00E-12 1.73 1.e5 1.00E-10 1. 7 0.2 0.1 1. 0.01 7 0.2 0.11 8.5e-4 1.e10 1. sdbnd 2 2400. 0.3 1.00E-12 1.00E-12 1.00E-12 1.73 1.e5 1.00E-10 1. 7 0.2 0.1 1. 0.01 7 0.2 0.11 8.5e-4 1.e10 1. wt 2 2400. 0.3 1.00E-12 1.00E-12 1.00E-12 1.73 935.8 1.00E-10 1. 5 1 0. 0. 1. PARAM 123456789012345678901234 8 3 100 10010000010002000040 03000 0.00e-05 4.3200E+05 1. 9.8066 1.e-5 1.000000E+05 0.000000E+00 0.000000E+00 0.000000E+00 1.050000E+01 1.500000E+01 TIMES----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8 3 1 4.320e+04 8.640E+04 4.320e+05 MULTI----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8 5 5 2 8 SELEC----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8 6 1 1 0.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+00 0.0000E+000.0000E+000.0000E+000.0000E+00 0.0000E+00 0.3303E+060.2220E+030.0000E+000.0000E+00 0.1000E-07 DIFFU----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8 1.000E-05 1.000E-10 1.000E-05 1.000E-10 1.000E-05 1.000E-10 1.000E-05 1.000E-10 1.000E-05 1.000E-10 FOFT ----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8 A12 1 AV1 1 COFT ----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8 A11 1A12 1 START----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8 GENER----1----+----2----+----3----+----4----+--- Cp=835.0 J/kg/K --7----+----8 AQ1 1 COM3 2.8100E-051.2520E+04 ENDCY MESHMAKER1----*----2----*----3----*----4----*----5----*----6----*----7----*----8 XYZ 0.00 NX 1 1. NY 1 .05 NY 49 .1 NZ 1 1.e-9 NZ 50 .1 NZ 1 2.e-9 ENDFI----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8

Figure 4. Input file SAM7CA2 for CO2 injection into shallow vadose zone.

39 Rev. 1.1

AWX 1( 56, 7) ST = 0.398556E+06 DT = 0.542880E+05 DX1= 0.344122E+01 DX2= 0.000000E+00 T = 15.000 P = 100258. S = 0.401320E-03 ICURV=0 ...ITERATING... AT [ 57, 1] --- DELTEX = 0.334440E+05 MAX. RES. = 0.794342E-01 AT ELEMENT AVO 1 EQUATION 3 ...ITERATING... AT [ 57, 2] --- DELTEX = 0.334440E+05 MAX. RES. = 0.546936E-01 AT ELEMENT AWW 1 EQUATION 1 ...ITERATING... AT [ 57, 3] --- DELTEX = 0.334440E+05 MAX. RES. = 0.488744E-02 AT ELEMENT AWX 1 EQUATION 1 ...ITERATING... AT [ 57, 4] --- DELTEX = 0.334440E+05 MAX. RES. = 0.142935E-04 AT ELEMENT AWX 1 EQUATION 1 AWX 1( 57, 5) ST = 0.432000E+06 DT = 0.334440E+05 DX1= 0.439866E+01 DX2= 0.000000E+00 T = 15.000 P = 100263. S = 0.629840E-03 ICURV=0 ^L simple soil for shallow CO2 release by perforated pipe. OUTPUT DATA AFTER ( 57, 5)-2-TIME STEPS THE TIME IS 0.500000E+01 DAYS @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ TOTAL TIME KCYC ITER ITERC KON DX1M DX2M DX3M MAX. RES. NER KER DELTEX 0.432000E+06 57 5 306 2 0.26870E+02 0.00000E+00 0.24887E-03 0.23839E-09 1696 1 0.33444E+05 @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ NCG = CO2 ELEM. INDEX P T SL XBRINE(LIQ) XNCG(LIQ) XAIR(LIQ) XAIR(GAS) XNCG(GAS) XTRC(GAS) DG (PA) (DEG-C) (KG/M**3) A11 1 1 0.10010E+06 0.15000E+02 0.50000E+00 0.00000E+00 0.20551E-62 0.15816E-04 0.98933E+00 0.15920E-59 0.00000E+00 0.12024E+01 A21 1 2 0.10013E+06 0.15000E+02 0.50187E+00 0.00000E+00 0.55279E-03 0.11310E-04 0.61716E+00 0.37355E+00 0.00000E+00 0.13804E+01 A31 1 3 0.10018E+06 0.15000E+02 0.50558E+00 0.00000E+00 0.11972E-02 0.60607E-05 0.28783E+00 0.70410E+00 0.00000E+00 0.15896E+01 A41 1 4 0.10023E+06 0.15000E+02 0.50930E+00 0.00000E+00 0.15542E-02 0.31547E-05 0.13976E+00 0.85272E+00 0.00000E+00 0.17066E+01 A51 1 5 0.10028E+06 0.15000E+02 0.51309E+00 0.00000E+00 0.17454E-02 0.16023E-05 0.68515E-01 0.92424E+00 0.00000E+00 0.17698E+01 A61 1 6 0.10032E+06 0.15000E+02 0.51700E+00 0.00000E+00 0.18452E-02 0.79471E-06 0.33369E-01 0.95952E+00 0.00000E+00 0.18032E+01 A71 1 7 0.10037E+06 0.15000E+02 0.52107E+00 0.00000E+00 0.18964E-02 0.38437E-06 0.15989E-01 0.97697E+00 0.00000E+00 0.18206E+01 A81 1 8 0.10042E+06 0.15000E+02 0.52533E+00 0.00000E+00 0.19224E-02 0.18085E-06 0.74862E-02 0.98550E+00 0.00000E+00 0.18297E+01 A91 1 9 0.10047E+06 0.15000E+02 0.52980E+00 0.00000E+00 0.19354E-02 0.82495E-07 0.34060E-02 0.98960E+00 0.00000E+00 0.18346E+01 AA1 1 10 0.10053E+06 0.15000E+02 0.53452E+00 0.00000E+00 0.19422E-02 0.36340E-07 0.14981E-02 0.99152E+00 0.00000E+00 0.18375E+01 AB1 1 11 0.10058E+06 0.15000E+02 0.53950E+00 0.00000E+00 0.19459E-02 0.15388E-07 0.63369E-03 0.99239E+00 0.00000E+00 0.18394E+01 AC1 1 12 0.10065E+06 0.15000E+02 0.54478E+00 0.00000E+00 0.19482E-02 0.62299E-08 0.25635E-03 0.99278E+00 0.00000E+00 0.18410E+01 AD1 1 13 0.10071E+06 0.15000E+02 0.55040E+00 0.00000E+00 0.19500E-02 0.23971E-08 0.98561E-04 0.99294E+00 0.00000E+00 0.18424E+01 AE1 1 14 0.10079E+06 0.15000E+02 0.55639E+00 0.00000E+00 0.19516E-02 0.87048E-09 0.35764E-04 0.99301E+00 0.00000E+00 0.18438E+01 AF1 1 15 0.10087E+06 0.15000E+02 0.56281E+00 0.00000E+00 0.19533E-02 0.29599E-09 0.12151E-04 0.99304E+00 0.00000E+00 0.18453E+01 AG1 1 16 0.10096E+06 0.15000E+02 0.56971E+00 0.00000E+00 0.19551E-02 0.93407E-10 0.38310E-05 0.99305E+00 0.00000E+00 0.18470E+01 AH1 1 17 0.10106E+06 0.15000E+02 0.57717E+00 0.00000E+00 0.19571E-02 0.27109E-10 0.11107E-05 0.99306E+00 0.00000E+00 0.18489E+01 AI1 1 18 0.10117E+06 0.15000E+02 0.58531E+00 0.00000E+00 0.19594E-02 0.71842E-11 0.29402E-06 0.99307E+00 0.00000E+00 0.18510E+01 AJ1 1 19 0.10131E+06 0.15000E+02 0.59425E+00 0.00000E+00 0.19620E-02 0.17442E-11 0.71288E-07 0.99308E+00 0.00000E+00 0.18535E+01 AK1 1 20 0.10147E+06 0.15000E+02 0.60418E+00 0.00000E+00 0.19651E-02 0.40276E-12 0.16435E-07 0.99309E+00 0.00000E+00 0.18565E+01 AL1 1 21 0.10166E+06 0.15000E+02 0.61524E+00 0.00000E+00 0.19689E-02 0.99191E-13 0.40398E-08 0.99311E+00 0.00000E+00 0.18601E+01 AM1 1 22 0.10191E+06 0.15000E+02 0.62731E+00 0.00000E+00 0.19738E-02 0.30522E-13 0.12401E-08 0.99312E+00 0.00000E+00 0.18647E+01 AN1 1 23 0.10223E+06 0.15000E+02 0.63963E+00 0.00000E+00 0.19802E-02 0.11710E-13 0.47425E-09 0.99314E+00 0.00000E+00 0.18707E+01 AO1 1 24 0.10268E+06 0.15000E+02 0.65033E+00 0.00000E+00 0.19891E-02 0.48231E-14 0.19446E-09 0.99318E+00 0.00000E+00 0.18791E+01 AP1 1 25 0.10338E+06 0.15000E+02 0.65557E+00 0.00000E+00 0.20028E-02 0.20180E-14 0.80807E-10 0.99322E+00 0.00000E+00 0.18921E+01 AQ1 1 26 0.10463E+06 0.15000E+02 0.64689E+00 0.00000E+00 0.20274E-02 0.10019E-14 0.39636E-10 0.99330E+00 0.00000E+00 0.19153E+01 AR1 1 27 0.10379E+06 0.15000E+02 0.68041E+00 0.00000E+00 0.20108E-02 0.94049E-13 0.37513E-08 0.99325E+00 0.00000E+00 0.18996E+01 AS1 1 28 0.10339E+06 0.15000E+02 0.70535E+00 0.00000E+00 0.20030E-02 0.24480E-11 0.98019E-07 0.99322E+00 0.00000E+00 0.18923E+01 AT1 1 29 0.10317E+06 0.15000E+02 0.72712E+00 0.00000E+00 0.19986E-02 0.31993E-10 0.12838E-05 0.99321E+00 0.00000E+00 0.18882E+01

Figure 5. Portion of output file for the shallow vadose zone problem SAM7CA2.

40 Rev. 1.1

(a)

(b)

(c)

(d)

Figure 6. EOS7CA simulation results for the SAM7CA2 vadose zone problem showing discretization and locations of injection well and water table (a), and color contours of CO2 mass fraction in the gas phase and light blue lines of aqueous phase saturation at (b) 0.5 days, (c) 1 day, and (d) 5 days.

41 Rev. 1.1

6. Final Notes

Summary of important points to remember in using EOS7CA:

• Users should have access to the TOUGH2 User’s Guide (Pruess et al., 2011)

for supplementary general TOUGH2 information.

• NKIN controls the type of INCON file or block to be read from. For NKIN =

NK, the INCON file is expected to be in the EOS7CA format with up to six

primary variables. For NKIN = 2 or 3, the INCON is expected to be in standard

EOS7 format with up to four primary variables.

• MOP(20) selects whether to reset variables to ensure that negative mass fractions

do not occur (see p. 20 of this report for details).

• The SELEC parameters IE(14), IE(15), and IE(16) control the enthalpy

calculation, the equation of state, and the choice of NCG, respectively.

• Although the gas mixture densities are very accurate in EOS7CA, no effects

of dissolved gas components on liquid density are included.

• The intended application area of EOS7CA is shallow (e.g., vadose zone) flow of

NCG (CO2, N2, or CH4) with a gas tracer, air, and water vapor. The part of the gas

phase that is not made up of NCG, tracer, and water vapor is assumed to be air.

• If molecular diffusivity is input as a negative number, the absolute value of

this number is used for the phase molecular diffusivity without modification by S

and τ (saturation and tortuosity) and without pressure or temperature effects.

• Pressure (P) affects gas diffusivity by the factor 1.0 × 105/P (Pruess et al., 2011).

For example, if pressure is 2.0 × 105 Pa, the effective molecular diffusivity for the

42 Rev. 1.1

gas is one-half the input value.

• Temperature affects gas diffusivity by the factor ((T + 273.15)/273.15)TEXP

(Pruess et al., 1999; 2011). If TEXP is input as zero, temperature effects on gas

diffusivity are neglected.

Acknowledgments

This work was carried out under the Zero Emissions Research and Technology project

funded by the Assistant Secretary for Fossil Energy, Office of Coal and Power Systems through

the National Energy Technology Laboratory, and by Lawrence Berkeley National Laboratory

under Department of Energy Contract No. DE-AC03-76SF00098. We thank Stefan Finsterle and

Christine Doughty (LBNL) for internal reviews.

Nomenclature

d molecular diffusivity m2 s -1

H enthalpy J kg-1

Kh Henry’s coefficient Pa

MW molecular weight kg mole-1

NCG non-condensible gas

NEQ number of equations per grid block

NK number of mass components (species)

NKIN number of mass components (species) in INCON file or block

NPH maximum number of phases present

P pressure Pa

R gas constant (8.31433 J kg-1 ˚C-1) J kg-1 K-1

S phase saturation -

43 Rev. 1.1

t time sec.

T temperature ˚C, K

V volume m3

partial molar volume m3 mol-1

x mole fraction in the liquid phase -

X mass fraction -

y mole fraction in the gas phase -

Y Y-coordinate m

Z Z-coordinate m

Z Z factor (compressibility factor) -

Greek symbols

µ dynamic viscosity kg m-1 s -1

φ porosity –

ρ density kg m-3

τ tortuosity –

Subscripts and superscripts

aq aqueous phase

g gas phase

ig ideal gas

l, liq liquid

0 reference value

β phase

κ mass components

44 Rev. 1.1

References

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eos7ca version 1.0: tough2 module for gas migration in

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